Decorrelation-Based Feature Discovery: Glaucoma
Jose Tamez
2023-10-07
- 1 Effect of UPSTM-Based Decorrelation
on Feature Discovery
- 1.0.1 Loading the libraries
- 1.1 Material and Methods
- 1.2 The Data
- 1.3 Generaring the report
- 1.4 The heatmap of the data
- 1.5 The decorrelation
- 1.6 The heatmap of the decorrelated data
- 1.7 The correlation matrix after decorrelation
- 1.8 U-MAP Visualization of features
- 1.9 Univariate Analysis
- 1.10 Comparing ILAA vs PCA vs EFA
- 1.11 Effect on CAR modeling
1 Effect of UPSTM-Based Decorrelation on Feature Discovery
1.0.1 Loading the libraries
library("FRESA.CAD")
library(readxl)
library(igraph)
library(umap)
library(tsne)
library(entropy)
library(TH.data)
op <- par(no.readonly = TRUE)
pander::panderOptions('digits', 3)
pander::panderOptions('table.split.table', 400)
pander::panderOptions('keep.trailing.zeros',TRUE)1.1 Material and Methods
All variables are derived from a laser scanning image of the eye background taken by the Heidelberg Retina Tomograph. Most of the variables describe either the area or volume in certain parts of the papilla and are measured in four sectors (temporal, superior, nasal and inferior) as well as for the whole papilla (global). The global measurement is, roughly, the sum of the measurements taken in the four sector.
The observations in both groups are matched by age and sex to prevent any bias.
Source Torsten Hothorn and Berthold Lausen (2003), Double-Bagging: Combining classifiers by bootstrap aggregation. Pattern Recognition, 36(6), 1303–1309.
1.2 The Data
GlaucomaM {TH.data}
data("GlaucomaM")
pander::pander(table(GlaucomaM$Class))| glaucoma | normal |
|---|---|
| 98 | 98 |
GlaucomaM$Class <- 1*(GlaucomaM$Class=="glaucoma")1.2.0.1 Standarize the names for the reporting
studyName <- "GlaucomaM"
dataframe <- GlaucomaM
outcome <- "Class"
thro <- 0.80
TopVariables <- 10
cexheat = 0.251.3 Generaring the report
1.3.1 Libraries
Some libraries
library(psych)
library(whitening)
library("vioplot")
library("rpart")1.3.2 Data specs
pander::pander(c(rows=nrow(dataframe),col=ncol(dataframe)-1))| rows | col |
|---|---|
| 196 | 62 |
pander::pander(table(dataframe[,outcome]))| 0 | 1 |
|---|---|
| 98 | 98 |
varlist <- colnames(dataframe)
varlist <- varlist[varlist != outcome]
largeSet <- length(varlist) > 1500 1.3.3 Scaling the data
Scaling and removing near zero variance columns and highly co-linear(r>0.99999) columns
### Some global cleaning
sdiszero <- apply(dataframe,2,sd) > 1.0e-16
dataframe <- dataframe[,sdiszero]
varlist <- colnames(dataframe)[colnames(dataframe) != outcome]
tokeep <- c(as.character(correlated_Remove(dataframe,varlist,thr=0.99999)),outcome)
dataframe <- dataframe[,tokeep]
varlist <- colnames(dataframe)
varlist <- varlist[varlist != outcome]
iscontinous <- sapply(apply(dataframe,2,unique),length) >= 5 ## Only variables with enough samples
dataframeScaled <- FRESAScale(dataframe,method="OrderLogit")$scaledData1.4 The heatmap of the data
numsub <- nrow(dataframe)
if (numsub > 1000) numsub <- 1000
if (!largeSet)
{
hm <- heatMaps(data=dataframeScaled[1:numsub,],
Outcome=outcome,
Scale=TRUE,
hCluster = "row",
xlab="Feature",
ylab="Sample",
srtCol=45,
srtRow=45,
cexCol=cexheat,
cexRow=cexheat
)
par(op)
}
1.4.0.1 Correlation Matrix of the Data
The heat map of the data
if (!largeSet)
{
par(cex=0.6,cex.main=0.85,cex.axis=0.7)
#cormat <- Rfast::cora(as.matrix(dataframe[,varlist]),large=TRUE)
cormat <- cor(dataframe[,varlist],method="pearson")
cormat[is.na(cormat)] <- 0
gplots::heatmap.2(abs(cormat),
trace = "none",
# scale = "row",
mar = c(5,5),
col=rev(heat.colors(5)),
main = "Original Correlation",
cexRow = cexheat,
cexCol = cexheat,
srtCol=45,
srtRow=45,
key.title=NA,
key.xlab="|Pearson Correlation|",
xlab="Feature", ylab="Feature")
diag(cormat) <- 0
print(max(abs(cormat)))
}
[1]
0.9961105
1.5 The decorrelation
DEdataframe <- IDeA(dataframe,verbose=TRUE,thr=thro)
#>
#> mr mv
#> ag at as an ai eag
#> 0.9838710 0.9516129 0.8870968 0.9677419 0.9193548 0.7096774
#>
#> Included: 62 , Uni p: 0.002419355 , Base Size: 2 , Rcrit: 0.2004905
#>
#>
1 <R=0.996,thr=0.950>, Top: 10< 5 >[Fa= 10 ]( 10 , 16 , 0 ),<|><>Tot Used: 26 , Added: 16 , Zero Std: 0 , Max Cor: 0.946
#>
2 <R=0.946,thr=0.900>, Top: 7< 5 >[Fa= 10 ]( 7 , 14 , 10 ),<|><>Tot Used: 37 , Added: 14 , Zero Std: 0 , Max Cor: 0.892
#>
3 <R=0.892,thr=0.800>, Top: 11< 2 >[Fa= 17 ]( 11 , 14 , 10 ),<|><>Tot Used: 52 , Added: 14 , Zero Std: 0 , Max Cor: 0.799
#>
4 <R=0.799,thr=0.800>
#>
[ 4 ], 0.7689698 Decor Dimension: 52 Nused: 52 . Cor to Base: 29 , ABase: 62 , Outcome Base: 0
#>
varlistc <- colnames(DEdataframe)[colnames(DEdataframe) != outcome]
pander::pander(sum(apply(dataframe[,varlist],2,var)))3.03
pander::pander(sum(apply(DEdataframe[,varlistc],2,var)))0.678
pander::pander(entropy(discretize(unlist(dataframe[,varlist]), 256)))3.94
pander::pander(entropy(discretize(unlist(DEdataframe[,varlistc]), 256)))3.74
varratio <- attr(DEdataframe,"VarRatio")
pander::pander(tail(varratio))| La_as | La_ai | La_vbss | La_an | La_at | La_ag |
|---|---|---|---|---|---|
| 0.0366 | 0.0366 | 0.0219 | 0.0212 | 0.0108 | 0.00776 |
1.5.1 The decorrelation matrix
if (!largeSet)
{
par(cex=0.6,cex.main=0.85,cex.axis=0.7)
UPLTM <- attr(DEdataframe,"UPLTM")
gplots::heatmap.2(1.0*(abs(UPLTM)>0),
trace = "none",
mar = c(5,5),
col=rev(heat.colors(5)),
main = "Decorrelation matrix",
cexRow = cexheat,
cexCol = cexheat,
srtCol=45,
srtRow=45,
key.title=NA,
key.xlab="|Beta|>0",
xlab="Output Feature", ylab="Input Feature")
par(op)
}
1.5.2 Formulas Network
Displaying the features associations
par(op)
clustable <- c("To many variables")
transform <- attr(DEdataframe,"UPLTM") != 0
tnames <- colnames(transform)
colnames(transform) <- str_remove_all(colnames(transform),"La_")
transform <- abs(transform*cor(dataframe[,rownames(transform)])) # The weights are proportional to the observed correlation
fscore <- attr(DEdataframe,"fscore")
VertexSize <- fscore # The size depends on the variable independence relevance (fscore)
names(VertexSize) <- str_remove_all(names(VertexSize),"La_")
VertexSize <- 10*(VertexSize-min(VertexSize))/(max(VertexSize)-min(VertexSize)) # Normalization
VertexSize <- VertexSize[rownames(transform)]
rsum <- apply(1*(transform !=0),1,sum) + 0.01*VertexSize + 0.001*varratio[tnames]
csum <- apply(1*(transform !=0),2,sum) + 0.01*VertexSize + 0.001*varratio[tnames]
ntop <- min(10,length(rsum))
topfeatures <- unique(c(names(rsum[order(-rsum)])[1:ntop],names(csum[order(-csum)])[1:ntop]))
rtrans <- transform[topfeatures,]
csum <- (apply(1*(rtrans !=0),2,sum) > 1*(colnames(rtrans) %in% topfeatures))
rtrans <- rtrans[,csum]
topfeatures <- unique(c(topfeatures,colnames(rtrans)))
print(ncol(transform))[1] 52
transform <- transform[topfeatures,topfeatures]
print(ncol(transform))[1] 48
if (ncol(transform)>100)
{
csum <- apply(1*(transform !=0),1,sum)
csum <- csum[csum > 1]
csum <- csum + 0.01*VertexSize[names(csum)]
csum <- csum[order(-csum)]
tpsum <- min(20,length(csum))
trsum <- rownames(transform)[rownames(transform) %in% names(csum[1:tpsum])]
rtrans <- transform[trsum,]
topfeatures <- unique(c(rownames(rtrans),colnames(rtrans)))
transform <- transform[topfeatures,topfeatures]
if (nrow(transform) > 150)
{
csum <- apply(1*(rtrans != 0 ),2,sum)
csum <- csum + 0.01*VertexSize[names(csum)]
csum <- csum[order(-csum)]
tpsum <- min(130,length(csum))
csum <- rownames(transform)[rownames(transform) %in% names(csum[1:tpsum])]
csum <- unique(c(trsum,csum))
transform <- transform[csum,csum]
}
print(ncol(transform))
}
if (ncol(transform) < 150)
{
gplots::heatmap.2(transform,
trace = "none",
mar = c(5,5),
col=rev(heat.colors(5)),
main = "Red Decorrelation matrix",
cexRow = cexheat,
cexCol = cexheat,
srtCol=45,
srtRow=45,
key.title=NA,
key.xlab="|Beta|>0",
xlab="Output Feature", ylab="Input Feature")
par(op)
VertexSize <- VertexSize[colnames(transform)]
gr <- graph_from_adjacency_matrix(transform,mode = "directed",diag = FALSE,weighted=TRUE)
gr$layout <- layout_with_fr
fc <- cluster_optimal(gr)
plot(fc, gr,
edge.width = 2*E(gr)$weight,
vertex.size=VertexSize,
edge.arrow.size=0.5,
edge.arrow.width=0.5,
vertex.label.cex=(0.15+0.05*VertexSize),
vertex.label.dist=0.5 + 0.05*VertexSize,
main="Top Feature Association")
varratios <- varratio
fscores <- fscore
names(varratios) <- str_remove_all(names(varratios),"La_")
names(fscores) <- str_remove_all(names(fscores),"La_")
dc <- getLatentCoefficients(DEdataframe)
theCharformulas <- attr(dc,"LatentCharFormulas")
clustable <- as.data.frame(cbind(Variable=fc$names,
Formula=as.character(theCharformulas[paste("La_",fc$names,sep="")]),
Class=fc$membership,
ResidualVariance=round(varratios[fc$names],3),
Fscore=round(fscores[fc$names],3)
)
)
rownames(clustable) <- str_replace_all(rownames(clustable),"__","_")
clustable$Variable <- NULL
clustable$Class <- as.integer(clustable$Class)
clustable$ResidualVariance <- as.numeric(clustable$ResidualVariance)
clustable$Fscore <- as.numeric(clustable$Fscore)
clustable <- clustable[order(-clustable$Fscore),]
clustable <- clustable[order(clustable$Class),]
clustable <- clustable[clustable$Fscore >= -1,]
topv <- min(50,nrow(clustable))
clustable <- clustable[1:topv,]
}
pander::pander(clustable)| Formula | Class | ResidualVariance | Fscore | |
|---|---|---|---|---|
| mr | NA | 1 | 1.000 | 7 |
| an | + an - (1.956)mr | 1 | 0.021 | 0 |
| ag | + ag - (5.849)mr | 1 | 0.008 | -1 |
| as | + as - (1.384)mr | 1 | 0.037 | -1 |
| ai | + ai - (1.407)mr | 1 | 0.037 | -1 |
| eat | + eat - (1.027)mr | 1 | 0.161 | -1 |
| eas | + eas - (1.374)mr | 1 | 0.300 | -1 |
| vbsg | + vbsg - (2.978)vbrs | 2 | 0.204 | 5 |
| mdic | - (0.276)vbsg + mdic | 2 | 0.170 | 0 |
| vbst | - (0.178)vbsg + vbst | 2 | 0.167 | 0 |
| vbsn | - (0.292)vbsg + vbsn | 2 | 0.122 | -1 |
| vbsi | - (0.237)vbsg + vbsi | 2 | 0.104 | -1 |
| vbrt | - (0.947)vbst + vbrt | 2 | 0.056 | -1 |
| vbri | - (0.209)vbsg + vbri | 2 | 0.176 | -1 |
| emd | - (1.004)mdic + emd | 2 | 0.060 | -1 |
| vbrs | NA | 3 | 1.000 | 4 |
| vbrg | + vbrg - (3.348)vbrs | 3 | 0.037 | 0 |
| vbrn | - (1.106)vbrs + vbrn | 3 | 0.174 | -1 |
| abrg | + abrg - (5.498)vbrs | 4 | 0.262 | 4 |
| eag | + eag - (0.845)abrg | 4 | 0.156 | 0 |
| ean | - (0.378)eag + ean | 4 | 0.093 | -1 |
| abrt | - (0.165)abrg + abrt | 4 | 0.177 | -1 |
| abrs | - (0.246)abrg + abrs | 4 | 0.082 | -1 |
| abrn | - (0.346)abrg + abrn | 4 | 0.094 | -1 |
| abri | - (0.244)abrg + abri | 4 | 0.086 | -1 |
| mdg | NA | 5 | 1.000 | 4 |
| mdt | - (0.865)mdg + mdt | 5 | 0.155 | -1 |
| mds | - (1.090)mdg + mds | 5 | 0.063 | -1 |
| mdn | - (1.066)mdg + mdn | 5 | 0.259 | -1 |
| mdi | - (0.924)mdg + mdi | 5 | 0.126 | -1 |
| vasg | NA | 6 | 1.000 | 3 |
| vass | - (0.275)vasg + vass | 6 | 0.154 | -1 |
| vasn | - (0.531)vasg + vasn | 6 | 0.061 | -1 |
| vasi | - (0.177)vasg + vasi | 6 | 0.323 | -1 |
| varg | NA | 7 | 1.000 | 3 |
| vars | - (0.264)varg + vars | 7 | 0.133 | -1 |
| varn | - (0.431)varg + varn | 7 | 0.072 | -1 |
| vari | - (0.270)varg + vari | 7 | 0.139 | -1 |
| mhcs | NA | 8 | 1.000 | 2 |
| mhcg | + mhcg - (0.689)mhcs | 8 | 0.330 | -1 |
| phcs | - (0.877)mhcs + phcs | 8 | 0.224 | -1 |
| tmg | NA | 9 | 1.000 | 2 |
| tms | - (1.217)tmg + tms | 9 | 0.230 | -1 |
| tmi | - (1.044)tmg + tmi | 9 | 0.314 | -1 |
| mhct | NA | 10 | 1.000 | 1 |
| phct | - (0.845)mhct + phct | 10 | 0.251 | -1 |
par(op)
1.6 The heatmap of the decorrelated data
if (!largeSet)
{
hm <- heatMaps(data=DEdataframe[1:numsub,],
Outcome=outcome,
Scale=TRUE,
hCluster = "row",
cexRow = cexheat,
cexCol = cexheat,
srtCol=45,
srtRow=45,
xlab="Feature",
ylab="Sample")
par(op)
}
1.7 The correlation matrix after decorrelation
if (!largeSet)
{
cormat <- cor(DEdataframe[,varlistc],method="pearson")
cormat[is.na(cormat)] <- 0
gplots::heatmap.2(abs(cormat),
trace = "none",
mar = c(5,5),
col=rev(heat.colors(5)),
main = "Correlation after ILAA",
cexRow = cexheat,
cexCol = cexheat,
srtCol=45,
srtRow=45,
key.title=NA,
key.xlab="|Pearson Correlation|",
xlab="Feature", ylab="Feature")
par(op)
diag(cormat) <- 0
print(max(abs(cormat)))
}
[1]
0.799364
1.8 U-MAP Visualization of features
1.8.1 The UMAP on Raw Data
classes <- unique(dataframe[1:numsub,outcome])
raincolors <- rainbow(length(classes))
names(raincolors) <- classes
topvars <- univariate_BinEnsemble(dataframe,outcome)
lso <- LASSO_MIN(formula(paste(outcome,"~.")),dataframe,family="binomial")
topvars <- unique(c(names(topvars),lso$selectedfeatures))
pander::pander(head(topvars))hic, varg, vars, vari, tmi and phci
# names(topvars)
#if (nrow(dataframe) < 1000)
#{
datasetframe.umap = umap(scale(dataframe[1:numsub,topvars]),n_components=2)
# datasetframe.umap = umap(dataframe[1:numsub,varlist],n_components=2)
plot(datasetframe.umap$layout,xlab="U1",ylab="U2",main="UMAP: Original",t='n')
text(datasetframe.umap$layout,labels=dataframe[1:numsub,outcome],col=raincolors[dataframe[1:numsub,outcome]+1])
#}1.8.2 The decorralted UMAP
varlistcV <- names(varratio[varratio >= 0.01])
topvars <- univariate_BinEnsemble(DEdataframe[,varlistcV],outcome)
lso <- LASSO_MIN(formula(paste(outcome,"~.")),DEdataframe[,varlistcV],family="binomial")
topvars <- unique(c(names(topvars),lso$selectedfeatures))
pander::pander(head(topvars))hic, varg, phci, rnf, phcg and vbrs
varlistcV <- varlistcV[varlistcV != outcome]
# DEdataframe[,outcome] <- as.numeric(DEdataframe[,outcome])
#if (nrow(dataframe) < 1000)
#{
datasetframe.umap = umap(scale(DEdataframe[1:numsub,topvars]),n_components=2)
# datasetframe.umap = umap(DEdataframe[1:numsub,varlistcV],n_components=2)
plot(datasetframe.umap$layout,xlab="U1",ylab="U2",main="UMAP: After ILAA",t='n')
text(datasetframe.umap$layout,labels=DEdataframe[1:numsub,outcome],col=raincolors[DEdataframe[1:numsub,outcome]+1])
#}1.9 Univariate Analysis
1.9.1 Univariate
univarRAW <- uniRankVar(varlist,
paste(outcome,"~1"),
outcome,
dataframe,
rankingTest="AUC")
univarDe <- uniRankVar(varlistc,
paste(outcome,"~1"),
outcome,
DEdataframe,
rankingTest="AUC",
)
1.9.2 Final Table
univariate_columns <- c("caseMean","caseStd","controlMean","controlStd","controlKSP","ROCAUC")
##top variables
topvar <- c(1:length(varlist)) <= TopVariables
tableRaw <- univarRAW$orderframe[topvar,univariate_columns]
pander::pander(tableRaw)| caseMean | caseStd | controlMean | controlStd | controlKSP | ROCAUC | |
|---|---|---|---|---|---|---|
| vari | 0.04480 | 0.0368 | 0.1150 | 0.0543 | 0.1035 | 0.880 |
| varg | 0.17851 | 0.1170 | 0.4139 | 0.1967 | 0.0252 | 0.873 |
| vars | 0.04506 | 0.0314 | 0.1068 | 0.0596 | 0.0172 | 0.851 |
| tmi | 0.03664 | 0.1258 | -0.1097 | 0.1038 | 0.6980 | 0.832 |
| varn | 0.08224 | 0.0595 | 0.1774 | 0.0894 | 0.2533 | 0.830 |
| hic | 0.39863 | 0.1407 | 0.2114 | 0.1574 | 0.7659 | 0.822 |
| tmg | -0.03356 | 0.0885 | -0.1524 | 0.0927 | 0.5179 | 0.818 |
| phcg | -0.03546 | 0.0691 | -0.1216 | 0.0661 | 0.9359 | 0.818 |
| phci | 0.00898 | 0.0882 | -0.0937 | 0.0779 | 0.7638 | 0.814 |
| tms | 0.03959 | 0.1166 | -0.1192 | 0.1376 | 0.9756 | 0.808 |
topLAvar <- univarDe$orderframe$Name[str_detect(univarDe$orderframe$Name,"La_")]
topLAvar <- unique(c(univarDe$orderframe$Name[topvar],topLAvar[1:as.integer(TopVariables/2)]))
finalTable <- univarDe$orderframe[topLAvar,univariate_columns]
pander::pander(finalTable)| caseMean | caseStd | controlMean | controlStd | controlKSP | ROCAUC | |
|---|---|---|---|---|---|---|
| varg | 0.17851 | 0.11700 | 0.4139 | 0.1967 | 2.52e-02 | 0.873 |
| hic | 0.39863 | 0.14073 | 0.2114 | 0.1574 | 7.66e-01 | 0.822 |
| tmg | -0.03356 | 0.08846 | -0.1524 | 0.0927 | 5.18e-01 | 0.818 |
| phcg | -0.03546 | 0.06909 | -0.1216 | 0.0661 | 9.36e-01 | 0.818 |
| phci | 0.00898 | 0.08818 | -0.0937 | 0.0779 | 7.64e-01 | 0.814 |
| rnf | 0.13956 | 0.06764 | 0.2252 | 0.0975 | 2.25e-01 | 0.800 |
| phcn | 0.00692 | 0.07364 | -0.0717 | 0.0881 | 3.03e-01 | 0.796 |
| vart | 0.00640 | 0.00533 | 0.0146 | 0.0117 | 7.54e-04 | 0.777 |
| vbrs | 0.16142 | 0.09970 | 0.0861 | 0.1319 | 4.75e-06 | 0.773 |
| La_mdic | 0.07786 | 0.05356 | 0.0351 | 0.0380 | 1.36e-01 | 0.766 |
| La_vbrt | -0.02477 | 0.01482 | -0.0345 | 0.0204 | 2.83e-01 | 0.713 |
| La_as | -0.61158 | 0.02849 | -0.5903 | 0.0285 | 8.42e-01 | 0.709 |
| La_vbri | -0.01438 | 0.03870 | -0.0394 | 0.0364 | 8.08e-02 | 0.698 |
| La_eas | -0.72443 | 0.05906 | -0.7891 | 0.1222 | 4.93e-03 | 0.697 |
dc <- getLatentCoefficients(DEdataframe)
fscores <- attr(DEdataframe,"fscore")
pander::pander(c(mean=mean(sapply(dc,length)),total=length(dc),fraction=length(dc)/(ncol(dataframe)-1)))| mean | total | fraction |
|---|---|---|
| 2.07 | 42 | 0.677 |
theCharformulas <- attr(dc,"LatentCharFormulas")
topvar <- rownames(tableRaw)
finalTable <- rbind(finalTable,tableRaw[topvar[!(topvar %in% topLAvar)],univariate_columns])
orgnamez <- rownames(finalTable)
orgnamez <- str_remove_all(orgnamez,"La_")
finalTable$RAWAUC <- univarRAW$orderframe[orgnamez,"ROCAUC"]
finalTable$DecorFormula <- theCharformulas[rownames(finalTable)]
finalTable$fscores <- fscores[rownames(finalTable)]
finalTable$varratio <- varratio[rownames(finalTable)]
Final_Columns <- c("DecorFormula","caseMean","caseStd","controlMean","controlStd","controlKSP","ROCAUC","RAWAUC","fscores","varratio")
finalTable <- finalTable[order(-finalTable$ROCAUC),]
pander::pander(finalTable[,Final_Columns])| DecorFormula | caseMean | caseStd | controlMean | controlStd | controlKSP | ROCAUC | RAWAUC | fscores | varratio | |
|---|---|---|---|---|---|---|---|---|---|---|
| vari | NA | 0.04480 | 0.03683 | 0.1150 | 0.0543 | 1.04e-01 | 0.880 | 0.880 | NA | NA |
| varg | NA | 0.17851 | 0.11700 | 0.4139 | 0.1967 | 2.52e-02 | 0.873 | 0.873 | 3 | 1.0000 |
| vars | NA | 0.04506 | 0.03143 | 0.1068 | 0.0596 | 1.72e-02 | 0.851 | 0.851 | NA | NA |
| tmi | NA | 0.03664 | 0.12578 | -0.1097 | 0.1038 | 6.98e-01 | 0.832 | 0.832 | NA | NA |
| varn | NA | 0.08224 | 0.05953 | 0.1774 | 0.0894 | 2.53e-01 | 0.830 | 0.830 | NA | NA |
| hic | NA | 0.39863 | 0.14073 | 0.2114 | 0.1574 | 7.66e-01 | 0.822 | 0.822 | 0 | 1.0000 |
| tmg | NA | -0.03356 | 0.08846 | -0.1524 | 0.0927 | 5.18e-01 | 0.818 | 0.818 | 2 | 1.0000 |
| phcg | NA | -0.03546 | 0.06909 | -0.1216 | 0.0661 | 9.36e-01 | 0.818 | 0.818 | 0 | 1.0000 |
| phci | NA | 0.00898 | 0.08818 | -0.0937 | 0.0779 | 7.64e-01 | 0.814 | 0.814 | 1 | 1.0000 |
| tms | NA | 0.03959 | 0.11659 | -0.1192 | 0.1376 | 9.76e-01 | 0.808 | 0.808 | NA | NA |
| rnf | NA | 0.13956 | 0.06764 | 0.2252 | 0.0975 | 2.25e-01 | 0.800 | 0.800 | 0 | 1.0000 |
| phcn | NA | 0.00692 | 0.07364 | -0.0717 | 0.0881 | 3.03e-01 | 0.796 | 0.796 | 1 | 1.0000 |
| vart | NA | 0.00640 | 0.00533 | 0.0146 | 0.0117 | 7.54e-04 | 0.777 | 0.777 | 0 | 1.0000 |
| vbrs | NA | 0.16142 | 0.09970 | 0.0861 | 0.1319 | 4.75e-06 | 0.773 | 0.773 | 4 | 1.0000 |
| La_mdic | - (0.276)vbsg + mdic | 0.07786 | 0.05356 | 0.0351 | 0.0380 | 1.36e-01 | 0.766 | 0.785 | 0 | 0.1696 |
| La_vbrt | - (0.947)vbst + vbrt | -0.02477 | 0.01482 | -0.0345 | 0.0204 | 2.83e-01 | 0.713 | 0.709 | -1 | 0.0562 |
| La_as | + as - (1.384)mr | -0.61158 | 0.02849 | -0.5903 | 0.0285 | 8.42e-01 | 0.709 | 0.501 | -1 | 0.0366 |
| La_vbri | - (0.209)vbsg + vbri | -0.01438 | 0.03870 | -0.0394 | 0.0364 | 8.08e-02 | 0.698 | 0.803 | -1 | 0.1759 |
| La_eas | + eas - (1.374)mr | -0.72443 | 0.05906 | -0.7891 | 0.1222 | 4.93e-03 | 0.697 | 0.621 | -1 | 0.3001 |
1.10 Comparing ILAA vs PCA vs EFA
1.10.1 PCA
featuresnames <- colnames(dataframe)[colnames(dataframe) != outcome]
pc <- prcomp(dataframe[,iscontinous],center = TRUE,scale. = TRUE,tol=0.01) #principal components
predPCA <- predict(pc,dataframe[,iscontinous])
PCAdataframe <- as.data.frame(cbind(predPCA,dataframe[,!iscontinous]))
colnames(PCAdataframe) <- c(colnames(predPCA),colnames(dataframe)[!iscontinous])
#plot(PCAdataframe[,colnames(PCAdataframe)!=outcome],col=dataframe[,outcome],cex=0.65,cex.lab=0.5,cex.axis=0.75,cex.sub=0.5,cex.main=0.75)
#pander::pander(pc$rotation)
PCACor <- cor(PCAdataframe[,colnames(PCAdataframe) != outcome])
gplots::heatmap.2(abs(PCACor),
trace = "none",
# scale = "row",
mar = c(5,5),
col=rev(heat.colors(5)),
main = "PCA Correlation",
cexRow = 0.5,
cexCol = 0.5,
srtCol=45,
srtRow= -45,
key.title=NA,
key.xlab="Pearson Correlation",
xlab="Feature", ylab="Feature")
1.10.2 EFA
EFAdataframe <- dataframeScaled
if (length(iscontinous) < 2000)
{
topred <- min(length(iscontinous),nrow(dataframeScaled),ncol(predPCA)-1)
if (topred < 2) topred <- 2
uls <- fa(dataframeScaled[,iscontinous],nfactors=topred,rotate="varimax",warnings=FALSE) # EFA analysis
predEFA <- predict(uls,dataframeScaled[,iscontinous])
EFAdataframe <- as.data.frame(cbind(predEFA,dataframeScaled[,!iscontinous]))
colnames(EFAdataframe) <- c(colnames(predEFA),colnames(dataframeScaled)[!iscontinous])
EFACor <- cor(EFAdataframe[,colnames(EFAdataframe) != outcome])
gplots::heatmap.2(abs(EFACor),
trace = "none",
# scale = "row",
mar = c(5,5),
col=rev(heat.colors(5)),
main = "EFA Correlation",
cexRow = 0.5,
cexCol = 0.5,
srtCol=45,
srtRow= -45,
key.title=NA,
key.xlab="Pearson Correlation",
xlab="Feature", ylab="Feature")
}
1.11 Effect on CAR modeling
par(op)
par(xpd = TRUE)
dataframe[,outcome] <- factor(dataframe[,outcome])
rawmodel <- rpart(paste(outcome,"~."),dataframe,control=rpart.control(maxdepth=3))
pr <- predict(rawmodel,dataframe,type = "class")
ptab <- list(er="Error",detail=matrix(nrow=6,ncol=1))
if (length(unique(pr))>1)
{
plot(rawmodel,main="Raw",branch=0.5,uniform = TRUE,compress = TRUE,margin=0.1)
text(rawmodel, use.n = TRUE,cex=0.75)
ptab <- epiR::epi.tests(table(pr==0,dataframe[,outcome]==0))
}
pander::pander(table(dataframe[,outcome],pr))| 0 | 1 | |
|---|---|---|
| 0 | 83 | 15 |
| 1 | 11 | 87 |
pander::pander(ptab$detail[c(5,3,4,6),])| statistic | est | lower | upper | |
|---|---|---|---|---|
| 5 | diag.ac | 0.867 | 0.812 | 0.911 |
| 3 | se | 0.888 | 0.808 | 0.943 |
| 4 | sp | 0.847 | 0.760 | 0.912 |
| 6 | diag.or | 43.764 | 19.005 | 100.778 |
par(op)
par(xpd = TRUE)
DEdataframe[,outcome] <- factor(DEdataframe[,outcome])
IDeAmodel <- rpart(paste(outcome,"~."),DEdataframe[,c(outcome,varlistcV)],control=rpart.control(maxdepth=3))
pr <- predict(IDeAmodel,DEdataframe,type = "class")
ptab <- list(er="Error",detail=matrix(nrow=6,ncol=1))
if (length(unique(pr))>1)
{
plot(IDeAmodel,main="ILAA",branch=0.5,uniform = TRUE,compress = TRUE,margin=0.1)
text(IDeAmodel, use.n = TRUE,cex=0.75)
ptab <- epiR::epi.tests(table(pr==0,DEdataframe[,outcome]==0))
}
pander::pander(table(DEdataframe[,outcome],pr))| 0 | 1 | |
|---|---|---|
| 0 | 89 | 9 |
| 1 | 10 | 88 |
pander::pander(ptab$detail[c(5,3,4,6),])| statistic | est | lower | upper | |
|---|---|---|---|---|
| 5 | diag.ac | 0.903 | 0.853 | 0.941 |
| 3 | se | 0.898 | 0.820 | 0.950 |
| 4 | sp | 0.908 | 0.833 | 0.957 |
| 6 | diag.or | 87.022 | 33.739 | 224.456 |
par(op)
par(xpd = TRUE)
PCAdataframe[,outcome] <- factor(PCAdataframe[,outcome])
PCAmodel <- rpart(paste(outcome,"~."),PCAdataframe,control=rpart.control(maxdepth=3))
pr <- predict(PCAmodel,PCAdataframe,type = "class")
ptab <- list(er="Error",detail=matrix(nrow=6,ncol=1))
if (length(unique(pr))>1)
{
plot(PCAmodel,main="PCA",branch=0.5,uniform = TRUE,compress = TRUE,margin=0.1)
text(PCAmodel, use.n = TRUE,cex=0.75)
ptab <- epiR::epi.tests(table(pr==0,PCAdataframe[,outcome]==0))
}
pander::pander(table(PCAdataframe[,outcome],pr))| 0 | 1 | |
|---|---|---|
| 0 | 85 | 13 |
| 1 | 20 | 78 |
pander::pander(ptab$detail[c(5,3,4,6),])| statistic | est | lower | upper | |
|---|---|---|---|---|
| 5 | diag.ac | 0.832 | 0.772 | 0.881 |
| 3 | se | 0.796 | 0.703 | 0.871 |
| 4 | sp | 0.867 | 0.784 | 0.927 |
| 6 | diag.or | 25.500 | 11.891 | 54.684 |
par(op)1.11.1 EFA
EFAdataframe[,outcome] <- factor(EFAdataframe[,outcome])
EFAmodel <- rpart(paste(outcome,"~."),EFAdataframe,control=rpart.control(maxdepth=3))
pr <- predict(EFAmodel,EFAdataframe,type = "class")
ptab <- list(er="Error",detail=matrix(nrow=6,ncol=1))
if (length(unique(pr))>1)
{
plot(EFAmodel,main="EFA",branch=0.5,uniform = TRUE,compress = TRUE,margin=0.1)
text(EFAmodel, use.n = TRUE,cex=0.75)
ptab <- epiR::epi.tests(table(pr==0,EFAdataframe[,outcome]==0))
}
pander::pander(table(EFAdataframe[,outcome],pr))| 0 | 1 | |
|---|---|---|
| 0 | 88 | 10 |
| 1 | 16 | 82 |
pander::pander(ptab$detail[c(5,3,4,6),])| statistic | est | lower | upper | |
|---|---|---|---|---|
| 5 | diag.ac | 0.867 | 0.812 | 0.911 |
| 3 | se | 0.837 | 0.748 | 0.904 |
| 4 | sp | 0.898 | 0.820 | 0.950 |
| 6 | diag.or | 45.100 | 19.365 | 105.036 |
par(op)